112 LearnersLast updated on August 5th, 2025
Surface Area of Solid
A solid is a three-dimensional object that occupies space and has a surface. The surface area of a solid is the total area covered by all its outer surfaces. This includes any flat, curved, or irregular surfaces that make up the solid. In this article, we will explore the concept of surface area for various solids.
What is the Surface Area of a Solid?
The surface area of a solid is the total area occupied by the boundary or surface of the solid. It is measured in square units.
Solids can have flat surfaces, such as the faces of a cube, or curved surfaces, such as those of a sphere. Understanding the surface area of a solid involves calculating the area of all its external surfaces.
Different types of solids include prisms, cylinders, cones, and spheres, each with unique surface area formulas.
Surface Area of a Solid Formula
Different solids have different formulas to calculate their surface areas. These formulas depend on the shape and dimensions of the solid.
Below are some common solids and their surface area considerations:
Solids with flat surfaces: Calculate the area of each face and sum them up.
Solids with curved surfaces: Use specific formulas for the curved parts.
Combined solids: Consider both flat and curved areas in the calculation.
Surface Area of a Cylinder
A cylinder has two flat circular bases and a curved surface connecting them. The curved surface area is known as the lateral surface area, and the total surface area includes both the curved surface and the two bases.
The formulas are: Curved Surface Area of a Cylinder = 2πrh square units
Total Surface Area of a Cylinder = 2πr(r + h) square units
where r is the radius of the base, h is the height of the cylinder.
Surface Area of a Sphere
A sphere is a perfectly round solid with a single curved surface and no edges or vertices.
The surface area of a sphere is calculated using the formula: Surface Area of a Sphere = 4πr² square units
where r is the radius of the sphere.
Surface Area of a Prism
A prism has two parallel bases and rectangular lateral faces.
The total surface area is the sum of the areas of all its faces.
For a rectangular prism, the formula is: Total Surface Area = 2lw + 2lh + 2wh square units where l is the length, w is the width, and h is the height.
Confusion between Lateral and Total Surface Area
Students often confuse lateral surface area with total surface area. Lateral surface area refers only to the sides of a solid, excluding the bases, while total surface area includes all surfaces. Ensure clarity of which area needs calculation.
Mistake 1
Using Incorrect Formulas
Using the wrong formula for a particular solid often leads to errors. Always verify the solid type and use the corresponding formula for that solid's surface area.
Mistake 2
Misidentifying Dimensions
Students sometimes confuse dimensions like radius with diameter or height with slant height. Carefully identify each dimension before substituting values into formulas.
Mistake 3
Forgetting to Include All Surfaces
When calculating total surface area, students may forget to include certain surfaces, such as the bases of a cylinder. Always verify that all surfaces are accounted for in the total calculation.
Mistake 4
Incorrect Calculation of π
A common mistake is using an inaccurate value for π. Use values like 3.14 or 22/7 for precision in calculations involving circles.
Mistake 5
Solved Examples of Surface Area of Solid
Find the curved surface area of a cylinder with a radius of 5 cm and a height of 12 cm.
CSA = 377 cm²
Problem 1
Given r = 5 cm, h = 12 cm. Use the formula: CSA = 2πrh = 2 × 3.14 × 5 × 12 = 377 cm²
Find the total surface area of a sphere with a radius of 7 cm.
Explanation
TSA = 615.44 cm²
Problem 2
Use the formula: TSA = 4πr² = 4 × 3.14 × 7² = 4 × 3.14 × 49 = 615.44 cm²
A rectangular prism has dimensions of length 8 cm, width 4 cm, and height 3 cm. Find the total surface area.
Explanation
TSA = 136 cm²
Problem 3
Use the formula: TSA = 2lw + 2lh + 2wh = 2(8 × 4) + 2(8 × 3) + 2(4 × 3) = 64 + 48 + 24 = 136 cm²
Find the surface area of a cone with a radius of 3 cm and a slant height of 8 cm.
Explanation
CSA = 75.36 cm²
Problem 4
CSA = πrl = 3.14 × 3 × 8 = 75.36 cm²
The total surface area of a cylinder is 282.6 cm² with a height of 6 cm. Find the radius.
Explanation
Radius = 3 cm
It is the total area that covers the external surfaces of a solid, including any flat, curved, or irregular surfaces.
1.What are the types of surface area calculations in solids?
2.How does slant height differ from height?
3.Is curved surface area always different from lateral surface area?
4.What unit is surface area measured in?
Common Mistakes and How to Avoid Them in Calculating Surface Area of Solids
Students often make mistakes while calculating the surface area of various solids, which leads to incorrect results. Below are some common mistakes and ways to avoid them.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
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: She has songs for each table which helps her to remember the tables
